On the Hadwiger numbers of centrally symmetric starlike disks

Zsolt Lángi

Abstract: The Hadwiger number $H(S)$ of a topological disk $S$ in ${\mathbb R}^2$ is the maximal number of pairwise nonoverlapping translates of $S$ that touch $S$. A conjecture of A. Bezdek., K. and W. Kuperberg [BKK] states that this number is at most eight for any starlike disk. A. Bezdek [B] proved that the Hadwiger number of a starlike disk is at most seventy five. In this note, we prove that the Hadwiger number of any centrally symmetric starlike disk is at most twelve.